How to cut grooves in a rectangle
Select the face where you want to add the groove. Press I to inset a new face. Then scale it with S and constrain to a axis (for me it was the X axis), press E to extrude the groove.


Or if you want the groove running all the way across the side, add two loop cuts with CtrlR. Then push them closer, by scaling same as above. After you have it the size you want, select the two outside faces and E extrude them out.